This first approach assumes that you don't care about "tracking" the large file; and consequently don't care to keep a copy of it on GitHub. In that case, you'll need to "go back in time" to an earlier commit; to a commit before you added the large, offending file.

You can do the following to do that:

git tag too_big # a "savepoint" just in case you care for it later
git log # find an earlier COMMIT_ID
git reset --hard COMMIT_ID # replace COMMIT_ID with the one found
# See how things are at this point
git status

If it's not clean after "git status", maybe you'd be interested in:

# Optionally, this will wipe things out
git clean -df

And then continuing your work from that point.

git push master # assuming your branch is master

The tag will give you a point of reference if you ever need to restore that giant file. It will also cause problems when you try to push to GitHub, and thus, push only master as opposed to a general purpose (ambiguous) git push (possibly implying --all).

Alternatively, if you must apply "source code control" to the very large file for some reason, you can explore GitHub's LFS (Large File Storage) git extension.